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Analysis of Bivariate Data - I aim to investigate the relationship between score in the P1 mock paper and score in the P1 exam. My population is lower sixth students at Peter Symonds College.

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Introduction

Aidan Russell-Gear                Page  of

S2 Coursework – Analysis of Bivariate Data

Introduction

        I aim to investigate the relationship between score in the P1 mock paper and score in the P1 exam. My population is lower sixth students at Peter Symonds College; I have obtained a table of 304 students which tells me their maths A-level course, gender, average GCSE score, results in P1 tests 1 and 2, P1 mock and P1 exam, from the college maths department.

        I wish to investigate this relationship so that my results may be used in the future by teachers and students to assess whether it is fair to base a prediction of the likely P1 exam score on the P1 mock result. I hope this will prove useful in deciding future options and motivating students to self-improvement. I hope then to prove convincingly whether the P1 exam result is correlated with the P1 mock result, and to what extent is this correlation.

        From my population of 304 students I took a sample of 50 to analyse for ease of calculation, I obtained this group by a simple random sample method. I assigned a random number to each student, then sorted the data in descending order and took the first 50 students as my sample.

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Middle

Pearson’s product moment correlation coefficient:

        And so the value of r was found to be 0.798922, and we see this result is a strong indication of positive correlation. However, this is merely my informed opinion, in order to get a more definitive answer to whether these two variables are correlated we must perform a hypothesis test.

Hypothesis Test

        To do this I must use the tables of critical values found in the MEI student handbook. These are standard pre-calculated values which will indicate whether or not my data are correlated, again assuming random normal distribution.

        My starting hypothesis, the null hypothesis (H0), is that there is no correlation between the P1 mock and P1 result in the population at all, my second (H1) is that there is some positive correlation. It is clear that there is no negative correlation and so I can merely look at the probabilities of positive correlation. I will perform a hypothesis test against the correlation coefficient of the parent population, ρ, my value of r is an estimate to ρ taken from a sample of the parent population.

                H0:        ρ = 0

                H1:        ρ > 0

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Conclusion

Note that my population was only from one year at Peter Symonds College and students could vary from year to year, though this is unlikely to be significant. However when performing the hypothesis test I assumed that my correlation coefficient was a good estimate for ρ, the parent correlation coefficient, and this was central to the validity of the hypothesis testing as a method of analysis. I feel that this is acceptable due to the high nature of the calculated correlation coefficient compared to the critical values for ρ calculated at 5% and at 0.5%, thus I feel that any error can be accommodated by the significantly larger value of the calculated coefficient than the critical value. This difference is so large that I am convinced of the validity of the relationship.

Bibliography

        The following sources were used in my in my investigation:

MEI Structured Mathematics – Statistics 2 (second edition)

MEI Structured Mathematics – Students’ Handbook

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